Warrington College of Business, University of Florida
This issue of The Journal of Risk covers topics including the estimation of value-at-risk using high-frequency data, as well as autoregressive techniques, the tail evaluation of extreme drawdowns, and the optimal selection of retained insurance loss when insurers and the insured differ in their beliefs.
In the issue’s first paper, “Conditional and unconditional intraday value-at-risk models: an application to high-frequency tick-by-tick exchange-traded fund data”, Houmera Bibi Sabera Nunkoo, Noor-Ul-Hacq Sookia, Preethee Nunkoo Gonpot and Thekke Variyam Ramanathan contrast unconditional approaches (based on three skewed distributions) and conditional approaches (based on the autoregressive conditional duration generalized autoregressive conditional heteroscedasticity (ACD-GARCH) model) to estimate intraday values-at-risk (IVaRs) with tick-bytick data. Using unconditional independence and conditional coverage backtesting tests, they show empirically the superiority of the unconditional approach for forecasting IVaR.
“Realized quantity extended conditional autoregressive value-at-risk models” by Pit Götz, the second paper in this issue, considers extensions of the conditional autoregressive value-at-risk (CAViaR) model that incorporate realized measures. By considering a variety of realized quantities and environment settings, the author provides empirical evidence showing the superiority of extensions of the asymmetric slope model and of the symmetric absolute value model in forecasting VaR.
Next, in “Peak-to-valley drawdowns: insights into extreme path-dependent market risk”, Hans Geboers, Benoit Depaire and Stefan Straetmans extend the study of drawdowns from their typical time window of consecutive days (where a trough is compared to the last peak) to a much longer window (where it is compared to the highest peak). This allows the authors to capture the cumulative effect of negative returns over several periods, thus offering insights into long-term risk. Geboers et al focus in particular on the tail behavior of maximum drawdowns and illustrate empirically the contrast between various asset classes, including equities, metal commodities, foreign currencies and cryptocurrencies.
In our fourth and final paper, Yanhong Chen, Wenjun Jiang and Yiying Zhang, the authors of “Mean–variance insurance design under heterogeneous beliefs”, address the mean–variance optimization of retained losses by an insured whose insurer’s beliefs differ. They consider, in particular, the singular case when one party assigns a zero probability to an event while the other does not. In their framework, Chen et al derive an optimal insurance policy that is Pareto optimal and that, given its accounting of belief heterogeneity, differs from those obtained through distortionrisk- measure and expected utility settings. Their approach can also be used to generate an efficient frontier to capture trade-offs associated with various degrees of aversion to retained loss.
Conditional and unconditional intraday value-at-risk models: an application to high-frequency tick-by-tick exchange-traded fund data
The authors consider conditional and unconditional intraday value-at-risk models for high-frequency exchange-traded funds, providing results useful to practitioners of high-frequency trading.
The author presents models for improved Value-at-Risk forecasts and joint forecasts of Value at Risk and Expected Shortfall and demonstrates that high-frequency-data-based realized quantities lead to better forecasts.
The authors investigate risk in relation to peak-to-valley market drawdowns and aim to gain insights into the drawdown behaviour of asset classes across time intervals.
The authors investigate a problem of optimal insurance in which the insured and the insure hold heterogenous beliefs concerning loss distribution and demonstrate their results with analytical and numerical examples.